The investigated setup consists of two conducting, charged spheres with radius
The electrostatic problem (no time dependency) consists of the two PEC spheres; the midpoints are separated by
The model can be easily constructed and simulated with CST EM STUDIO®, the low frequency and statics module of CST STUDIO SUITE®.
The CAD modeler has a predefined object ‘Sphere’ and so the setup is quickly done. The option of a potential definition can be found in the simulation ribbon. By choosing open boundary conditions, appropriate symmetry planes and a tetrahedral mesh with curved elements, the simulation can be fast and accurately performed. In order to improve the accuracy of the simulation, a vacuum sphere is defined around each PEC sphere, with a radius
|R0||1 m||PEC sphere radius|
|distance||5 m||Seperation of sphere midpoints|
|U||1 V||Potential between spheres|
In order to extract the field value at a certain point in the 3 dimensional calculation domain, the 3d post processing template "Evaluate field in arbitrary coordinates" is used.
The provided images show the results in a 2D cut-plane. From the absolute field pattern, it is clear that the highest electric field is at the inner faces of the two spheres. The vector plot helps to understand the field distribution. The arrows are always perpendicular to the PEC surfaces, indicating that the field is normal to the surface of the spheres, and the open boundaries of the simulation setup have no visual influence on the direction and strength of the fields close to the boundaries of the calculation domain.
By varying the distance between spheres, the maximum field strength can plotted vs the distance as shown in Figure 5. It can be seen that the analytical value
Will the electric field introduce a force on the spheres? If so, in which direction does it point? Use the "Forces" tool under the post processing ribbon to calculate the force acting on the spheres relative to the origin.